Find the domain and range of the function.
-$$f ( x ) = - x ^ { 2 } - 8 x - 21$$
A) Domain: $( - \infty , \infty )$; Range: $( - \infty , 4 ]$
B) Domain: $( - \infty , \infty )$; Range: $( - \infty , - 5 ]$
C) Domain: $( - \infty , - 5 ]$; Range: $[ 4 , \infty )$
D) Domain: $( - \infty , \infty )$; Range: $[ 5 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers, $( - \infty , \infty )$. The range is determined by the vertex of the parabola, which is a maximum here due to the negative leading coefficient. The vertex is at $(-4, -5)$, so the range is $( - \infty , - 5 ]$.

Find the Domain and Range of the Function f(x)=−x2−8x−21f ( x ) = - x ^ { 2 } - 8 x - 21f(x)=−x2−8x−21

Find the Domain and Range of the Function $f ( x ) = - x ^ { 2 } - 8 x - 21$